You said th pumpm only runs "a second to prime the system" and that " there is no pressure sensor to let it know what the PSI of the system is".
Then you said "it will only run for a second to just build pressure". How's the PCM know when it's built pressure if there is no sensor?
Then you said "it can't build pressure if the line is disconnected" . Then why does it stop running? It hasn't built pressure and there is no fuel flowing.
How does the engine get its fuel when it is running then? Does it pull it from the tank or is there another pump?